Browsing by Author "Mutuku, Winfred Nduku"

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    A Model of Tuberculosis and DiabetesCo-Infection with Optimal Control
    (2023-12-30) Musyokia, Eunice Mueni; Mutuku, Winfred Nduku; Imbusi, Nancy Matendechere; Omondi, Evans Otieno
    Aims/ objectives:Tuberculosis and diabetes co-infection is a complex health issue, thus, effectivemanagement requires understanding disease dynamics and interactions. This paper expands the existingmodel to incorporate the co-infection of diabetes and tuberculosis to understand disease complications better.Methodology:The study employs the next-generation matrix to calculateRCand utilizes LaSalle’sinvariance principle. It demonstrates that the model achieves global asymptotic stability at the disease-free equilibrium (DFE) whenRC≤1. The Volterra-Lyapunov matrix is then employed to establish globalasymptotic stability of the endemic equilibrium whenRC>1. Based on the Jacobian matrix, local stabilityanalysis suggests the potential for epidemic eradication whenRC≤1, whileRC≥1indicates a risk ofepidemic spread. Numerical solutions using ODE45 in Matlab R2021b are employed for the analysis. Results:The sensitivity analysis highlighted the significant impact of TB transmission coefficientβanddiabetes acquisition rateα1onRC, emphasizing the need for optimal control measures targeting thesefactors.Conclusion:A decrease in TB transmission coefficient led to a reduction inRCfrom1.0863to0.1845,suggesting the potential effectiveness of control strategies. The study also recommends exploring modelsconsidering different diabetes types in future research.
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    Car Antifreeze and Coolant: Comparing Water and Ethylene Glycol as Nano Fluid Base Fluid
    (Sretech Journal of publication, 2018) Kimulu, Ancent Makau; Mutuku, Winfred Nduku; Mutua, Nicholas Muthama
    Most internal combustion engines are fluid cooled using liquid coolants mostly water and ethylene glycol, whose heat transfer capabilities are limited. An alternative for improving their thermophysical properties is the addition of metal oxides so as to make Nanofluids. This study investigates car antifreeze and coolants by comparing water-based and ethylene glycol based Nanofluids to determine the Nanofluid which provides optimum cooling. The governing equations are non–dimensionalised using similarity transformation and the resulting equations solved numerically using the Runge–Kutta fourth order scheme. Graphical results of pertinent parameters on fluid velocity, temperature, skin friction and rate of heat transfer are presented and discussed in depth putting into consideration the industrial application. It was observed that the magnetic field slows the fluid flow while increasing the fluid temperature. Also ethylene glycol Nanofluid offers better cooling capabilities.